Yes it is possible

In my OPINION baptism isn't necessarily real until you have made an independent decision whether or not to believe in a 'god'. If you were baptised at a young age or didn't have any sort of say in the matter and now that you're older feel like you need to undo something, there's nothing to undo...You are you and what you believe in is what you believe in. Not holy water can not change that, nor a priest, nor any sort of church. Don't let anyone dictate who you want to be or how you want to live your life.

It's just water and mumbo-jumbo if you're a non-believer.

A baptism is just water and prayer. It can be a powerful bond if you're part of your church. But if you're a non-believer (and I affirm your choice) then you can simply make up your own absurd little ritual to un-baptize yourself. Remember, religion is just a matter of faith, not fact.

Yes, it is possible to change my mind.

In the Catholic faith Baptism is usually done at a young age, before a child has the capacity to make a decision to commit to anything. To believe that it cannot be undone is to believe the Catholic Church has the right to determine a child's fate. The Catholic Church does say "once a Catholic, always a Catholic" as if any determination about one's own life is invalid against this sacrament that they performed, but that is absurd. The church can continue to consider you a Catholic if they choose to do so, but that is on their books alone.

Mentally, yes

Because I don't really believe that baptizing does any effect on a person (magical water? really?), the term "un-baptizing" means to me changing your belief. If someone was baptized and raised Christian, for example, that person can "un-baptize" him/herself and convert to another religion, like Muslim or agnosticism. Being baptized doesn't have to be you're doomed.

To an extent, at least.

Obviously, you can't actually reverse an act that has already been done. If you were baptized at one point, you've been baptized, and that's indisputable. However, the act of baptism is a symbol, and with this in mind, you can act against it on the same level. Symbolically, you can reject the meaning that the baptism had on you, through a declaration or rejection of what the baptism asserted. I'd generally argue that if you have left the church that baptized you, that counts as such a rejection.

No

Getting baptized is a public affirmation that you will live your life to follow the path of Jesus Christ. If you get cold feet, change your mind and want to live your own way, you can do so. But you can not go back in time and un-pledge your life to God. It would be like getting engaged to a woman or man and then 5 months before the planned wedding call it off. You can call the wedding off, but you can't go back in time and not get engaged.

No It's Not

Baptism is only symbolic anyway of a commitment to live and die with Christ and take his sacrifice. Once done, it's done. You can choose to leave the faith but you can't go back in time and change what happened. So it's not possible to unbaptize yourself, but it's not really something that has to be worried about since a person can and will always live life the way they choose.